The demo will perform exactly the same as the full sim, so if you are having problems, please do not buy the sim yet.
A crash in X‑Plane can be caused by a multitude of factors. If the automatic crash reporter comes up, be sure to send the report so Laminar Research has the data on your crash.
In general, a good place to start for almost any problem with X‑Plane is running the installer to update the program. Even if you are running the latest version of the simulator, the Installer/Updater can find missing or accidentally modified files and replace them with the correct default files.
If you are running the latest version of the simulator and still have problems, another good place to look is at the preferences. Move the preferences folder (found in the Output folder) to the desktop, then restart X‑Plane and default preferences will be restored. If the default preferences do not fix your problem, you can simply replace them with the folder you moved to the desktop and restore your personalized settings.
The final common culprit is third party add ons, such as scenery and plugins. Try moving the Custom Scenery folder and plugins folder (found in the Resources folder) to the desktop, then restart X-Plane.